Seiberg-Witten Transforms of Noncommutative Solitons

TL;DR

This paper evaluates the Seiberg-Witten map for noncommutative solitons and instantons, revealing how their properties translate into commutative variables and identifying their brane moduli.

Contribution

It provides explicit calculations of the Seiberg-Witten transform for solitons and instantons, clarifying their geometric and physical interpretations in commutative space.

Findings

Solitons have delta-function supports in commutative variables.

Instantons exhibit finite size determined by noncommutative scale and deformation parameter.

Large deformation parameter yields instanton profiles similar to BPST instantons.

Abstract

We evaluate the Seiberg-Witten map for solitons and instantons in noncommutative gauge theories in various dimensions. We show that solitons constructed using the projection operators have delta-function supports when expressed in the commutative variables. This gives a precise identification of the moduli of these solutions as locations of branes. On the other hand, an instanton solution in four dimensions allows deformation away from the projection operator construction. We evaluate the Seiberg-Witten transform of the U(2) instanton and show that it has a finite size determined by the noncommutative scale and by the deformation parameter \rho. For large \rho, the profile of the D0-brane density of the instanton agrees surprisingly well with that of the BPST instanton on commutative space.